Seminars and Colloquia by Series

Mathematical theory of structured deep neural networks

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 28, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ding-Xuan Zhou – School of Mathematics and Statistics, University of Sydney, Australia –

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, natural language processing, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But there is much less theoretical understanding about the modelling, approximation or generalization abilities of deep learning models with network architectures. An important family of structured deep neural networks is deep convolutional neural networks (CNNs) induced by convolutions. The convolutional architecture gives essential differences between deep CNNs and fully-connected neural networks, and the classical approximation theory for fully-connected networks developed around 30 years ago does not apply.  This talk describes approximation and generalization analysis of deep CNNs and related structured deep neural networks. 
 

Robust construction of the incipient infinite cluster in high-dimensional percolation

Series
Stochastics Seminar
Time
Thursday, April 24, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pranav Chinmay – CUNY graduate center –

The incipient infinite cluster was first proposed by physicists in the 1970s as a canonical example of a two-dimensional medium on which random walk is subdiffusive. It is the measure obtained in critical percolation by conditioning on the existence of an infinite cluster, which is a probability zero event. Kesten presented the first rigorous two-dimensional construction of this object as a weak limit of the one-arm event. In high dimensions, van der Hofstad and Jarai constructed the IIC as a weak limit of the two-point connection using the lace expansion. Our work presents a new high-dimensional construction which is "robust", establishing that the weak limit is independent of the choice of conditioning. The main tools used are Kesten's original two-dimensional construction combined with Kozma and Nachmias' regularity method. Our robustness allows for several applications, such as the explicit computation of the limiting distribution of the chemical distance, which forms the content of our upcoming project. This is joint work with Shirshendu Chatterjee, Jack Hanson, and Philippe Sosoe. The preprint can be found at https://arxiv.org/abs/2502.10882.

TBD

Series
Geometry Topology Seminar
Time
Monday, April 21, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Diana Hubbard – Brooklyn College, CUNY

TBD

TBD by Thomas Kahle

Series
Algebra Seminar
Time
Monday, April 21, 2025 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thomas Kahle – OvGU Magdeburg

Relations between rational functions and an analog of the Tits alternative

Series
Number Theory
Time
Wednesday, April 16, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tom Tucker – Rochester University –

Work of Levin and Przytycki shows that if two non-special rational
functions f and g of degree >1>1over CC share the same set of
preperiodic points, there are mm, nn, and rr such that fmgn=frfmgn=fr.
In other words, ff and gg nearly commute.  One might ask if there are
other sorts of relations non-special rational functions ff and gg over CC
might satisfy when they do not share the same set of preperiodic
points.  We will present a recent proof of Beaumont that shows that
they may not, that if f and g do not share the same set of preperiodic
points, then they generate a free semi-group under composition.  The
proof builds on work of Bell, Huang, Peng, and the speaker, and uses a
ping-pong lemma similar to the one used by Tits in his proof of the
Tits alternative for finitely generated linear groups.

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